FISHERY BULLETIN: VOL. 74, NO. 2 



In actual practice Nj is tabulated. N\i is then 

 estimated by rearranging the above expression: 



N', = N, 



where Nj = observed class frequency 



N'ci= edge corrected class frequency 

 k = extent of the observation window 



in meters (usually 250 m) 

 d = mean class diameter in meters. 



As an example, when using a 250-m observation 

 band, a 50-m target may be entirely detected over 

 200 m of that band, whereas a 100-m target must 

 occur within a band of only 150 m to be detected. 

 If one counts 10 50-m targets and 3 100-m 

 targets, the counts, when corrected for edge bias, 

 will be 10(250)/(250 - 50) = 12.5 and 3(250)/(250 

 - 100) = 5, respectively. 



Horizontal school area is calculated by multi- 

 plying A?^' by the area of a circle whose diameter is 

 equal to the class mark. The calculation is based 

 on the assumption that with an increasing sam- 

 ple size the school dimension perpendicular to the 

 ship's track will approximate the diameter of a 

 circle whose area is equal to the area of a given 

 school, however irregularly shaped. This assump- 

 tion contains the condition that the orientation of 

 a sample of schools is random and in no way re- 

 lated to that of the survey ship. 



The resulting cumulative frequency diagram 

 (Figure 2) would indicate that over 507c of the 

 schools are less than 30 m in diameter while 90% 

 of the horizontal school area is contributed by 

 schools larger than 30 m in diameter. Mais' (1974) 

 experience with over 23,000 schools (corrected for 

 edge bias) in the same survey area indicated a 

 similar distribution with a mode at 30 to 40 m 

 (Figures 2, 3). 



Smaller schools (<20 m in diameter) were 

 likely to be undersampled by both the National 

 Marine Fisheries Service (NMFS) and CF&G as 

 the probability of their detection decreases faster 

 with range than larger schools. Even if an expo- 

 nential model of target size obtains in nature, 

 schools smaller than 20 m would contribute little 

 in amounts of horizontal school area. 



The significance of a negative bias in the lower 

 end of the observed school size distribution may 

 be evaluated by fitting a power curve to that por- 

 tion of the distribution between 15 and 165 m. 



20 40 60 80 100 120 140 160 



Figure 2. — Cumulative frequencies of sonar-detected fish 

 schools by size and their contributing horizontal area (NMFS 

 data only). The two modes in the CF&G data curve, drawn 

 from a much larger sample (5x), might suggest either a sys- 

 tematic sampling error or optimum fish school sizes. 



The equation, derived by a least squares fit, as- 

 sumes the following form: 



y = ax . 



Using the NMFS sample of 4,355 targets: 

 AT', = 428,864 {D mX^-^''^ 



where A''', = edge-bias corrected target fre- 

 quency within class i 

 (Dm)i = mean diameter of class / in meters. 



-3 20 



o" 



_) 

 I- o 

 2 O 10 

 UJ I 

 o o 

 cr lo 



40 60 80 100 120 



MEAN CLASS DIAMETER (meters) 



Figure 3. — Percent of total school count by size class. NMFS 

 data are represented by the shaded bars; the 

 open bars are calculated from CF&G data. 



284 



